A hybrid electric vehicle can improve the energy efficiency of an engine of a vehicle and decrease the amount of exhaust emissions of the engine. The improvements in energy efficiency for hybrid electric vehicles is due in part to the regeneration of electric energy from vehicle kinetic energy while the vehicle is being braked.
A battery is an important part of a hybrid electric vehicle. The battery supplies power and stores remaining power. Unfortunately, the available power of the battery varies according to operating temperature, a state of charge (SOC), aging, or the like, thus making it is difficult to employ the battery in a hybrid electric vehicle.
The terminal voltage of the battery increases as the battery charges, and it decreases as the battery discharges. In addition, the terminal voltage of the battery also changes according to charging/discharging load, so it is quite difficult to model battery terminal voltage characteristics.
A battery cell terminal voltage Ucell of a battery cell in FIG. 1 can be obtained according to the following equation 1:                                           U            cell                    =                                    U              ocv                        -                                          1                C                            ⁢                              ∫                                                      I                    avg                                    ⁢                                      ⅆ                    t                                                                        -                          U              c                        -                                          U                d                            ⁡                              (                                  I                  avg                                )                                      -                                          (                                                                            R                      a                                        (                                                                  T                        BAT                                            ,                      …                                        ⁢                                                                                   )                                    +                                      R                    c                                                  )                            ×                              I                avg                                                    ,                            [                  Equation          ⁢                                           ⁢          1                ]            where Uocv is a no-load voltage (or a battery open-circuit voltage), Uc is a voltage variation due to load history, C is a capacitance, Iavg is an average current, Ud is a voltage drop due to dipoles (chemical activity) on the reactive surface, Ra is an electrolyte resistance, Rc is a conductor resistance, and TBAT is a battery temperature. The electrolyte resistance Ra changes according to an SOC, a battery temperature, and aging of the battery, and the conductor resistance Rc changes according to the aging of the battery.
In FIG. 2, an electric circuit that is equivalent to the battery cell of FIG. 1 is shown. Based on this equivalent circuit, a terminal voltage Vt can be obtained according to the following equation 2:                                           V            t                    =                                    V              oc                        -                                          I                t                            ×                              (                                                      R                    h                                    +                                                            R                      d                                        ×                                          (                                              1                        -                                                  ⅇ                                                                                                                    -                                t                                                            /                                                              R                                d                                                                                      ⁢                                                          C                              p                                                                                                                          )                                                                      )                                                    ,                            [                  Equation          ⁢                                           ⁢          2                ]            where Voc is an effective no load voltage, It is a charge (or discharge) current, Rh is an instantaneous resistance, Rd is a delayed resistance, and Cp is a parallel capacitance. The conductor resistance Rc contributed by the positive and negative terminals and a current collector can be expressed as the instantaneous resistance Rh. The electrolyte resistance is determined by Cp.
As can be observed from Equation 2, a precise calculation of the battery terminal voltage Vt as a function of time using the battery equivalent model shown in FIG. 2, is dependent upon knowledge of the capacitor value Cp. A precise capacitor value, however, is difficult to calculate because it changes according to load conditions and operating conditions.
Accordingly, what is needed is a method for determining a steady state battery terminal voltage under load and operating conditions.